Ryuji Sueoka gave East Bengal the 10th minute lead before Joaquim Abranches (40th) doubled the margin after a howler from Mohammedan Sporting defence.
Mohammedan Sporting had an instant reply with Joshimar D'Silva Martins heading one home after seeing East Bengal custodian Abhra Mondal out of place.
But that was their solitary moment of glory as Edeh Chidi (62nd) completed the rout after an offside Sueoka cleverly let the Nigerian go past him and convert into an open net for their first-ever successive win this season.
Laggards Mohammedan Sporting (18 from 21) look certain to be relegated and conclude their top tier sojourn that had come after four seasons.
Mohammedan Sporting have won two titles this season winning both the Durand Cup and the IFA Shield but their I-League performance has been below par as they have only managed one win in their last 13 fixtures having scored 19 goals from 21 matches.